Seminormalization and continuous rational functions on complex algebraic varieties
[Seminormalisation et fonctions rationnelles continues sur des variétés algébriques complexe]
Bernard, François1
1 Bâtiment Sophie Germain, Place Aurélie Nemours, 75013 Paris (France)
Annales de l'Institut Fourier, Online first, 42 p.

The seminormalization of an algebraic variety is the biggest variety which is link to it with a birational, finite and bijective morphism. In this paper, we bring a new understanding to the seminormalization of complex algebraic varieties. We show that it can be obtained by replacing the structural sheaf of the variety by the sheaf of rational functions which extends continuously for the Euclidean topology. We further study this type of functions which can be seen as complex regulous functions, a class of functions recently introduced in real algebraic geometry, or as the algebraic counterpart of c-holomorphic functions.

La seminormalisation d’une variété algébrique complexe est la plus grande variété qui soit liée à la variété de départ par un morphisme birationnel, fini et bijectif. Dans cet article, nous apportons une nouvelle compréhension à la seminormalization des variétés algébriques complexes. Nous montrons que celle-ci peut-être obtenue en remplaçant le faisceau structural de la variété par celui des fonctions rationnelles qui s’étendent continûment sur les points fermés, pour la topologie Euclidienne. Nous étudions plus en détail ce type de fonctions qui peuvent être vues comme la version complexe des fonctions régulues, récemment introduitent en géométrie algébrique réelle, ou bien comme la version algébrique des fonctions c-holomorphes

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DOI : 10.5802/aif.3739
Classification : 14M05, 13F45, 14B05
Keywords: seminormalization, rational continuous functions, regulous functions
Mots-clés : seminormalisation, fonctions rationnelles continues, fonctions régulues

Bernard, François 1

1 Bâtiment Sophie Germain, Place Aurélie Nemours, 75013 Paris (France) 
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Bernard, François. Seminormalization and continuous rational functions on complex algebraic varieties. Annales de l'Institut Fourier, Online first, 42 p.

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